1. **State the problem:** We need to calculate the magnitude of the electrostatic force between two charged particles. 2. **Formula used:** The electrostatic force between two point charges is given by Coulomb's law: $$F = k \frac{|q_1 q_2|}{r^2}$$ where: - $F$ is the magnitude of the force, - $k = 8.99 \times 10^9 \ \text{N m}^2/\text{C}^2$ is Coulomb's constant, - $q_1$ and $q_2$ are the charges, - $r$ is the distance between the charges. 3. **Given values:** - $q_1 = 3.00 \times 10^{-6} \ \text{C}$ - $q_2 = 1.50 \times 10^{-6} \ \text{C}$ - $r = 12.0 \ \text{cm} = 0.12 \ \text{m}$ (converted to meters) 4. **Calculate the force:** $$F = 8.99 \times 10^9 \times \frac{(3.00 \times 10^{-6})(1.50 \times 10^{-6})}{(0.12)^2}$$ 5. **Simplify numerator:** $$3.00 \times 10^{-6} \times 1.50 \times 10^{-6} = 4.50 \times 10^{-12}$$ 6. **Calculate denominator:** $$0.12^2 = 0.0144$$ 7. **Calculate force:** $$F = 8.99 \times 10^9 \times \frac{4.50 \times 10^{-12}}{0.0144} = 8.99 \times 10^9 \times 3.125 \times 10^{-10}$$ 8. **Multiply constants:** $$F = 2.81 \ \text{N}$$ **Final answer:** The magnitude of the electrostatic force between the particles is approximately $2.81$ newtons.